The ones talked about in TFA are three staged, with the third stage being liquid. Can you launch an orbital solid fueled rocket? I thought that liquid (oxygen) was needed.
It's hard to get precise velocity changes with a solid fuel rocket. So must orbital class rockets have a liquid fuel stage at the end. And most rockets don't use oxygen for a propellant, because that's cryogenic, and hard to keep liquid. So called storable propellants are frequently used, especially for military rockets. That said, the most launched rocket last year was a cryogenic fueled rocket.
US missiles are entirely solid fueled but they do not achieve orbit either. They spent short time exoatmospheric and then reenter, well, ballistically.